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The Statistical Imagination

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  1. The Statistical Imagination • Chapter 1. The Statistical Imagination © 2008 McGraw-Hill Higher Education

  2. The Field of Statistics • As a field of study, statistics is a set of procedures for gathering, measuring, classifying, coding, computing, analyzing, and summarizing systematically acquired numerical information © 2008 McGraw-Hill Higher Education

  3. Applications of Statistics • Scientific applications: A tool for testing scientific theories • Practical applications : Used by marketing advertisers, policy makers, public health officials, insurance underwriters, educators, survey firms, stock investors and analysts, and odds makers © 2008 McGraw-Hill Higher Education

  4. The Statistical Imagination • An appreciation of how usual or unusual an event, circumstance, or behavior is in relation to a larger set of similar events, and an appreciation of an event’s causes and consequences © 2008 McGraw-Hill Higher Education

  5. Features of the Statistical Imagination • It is a balanced way of observing the world • It involves the ability to think through a problem and maintain a sense of proportion when weighing evidence against preconceived notions • It helps us to understand that most events are predictable © 2008 McGraw-Hill Higher Education

  6. Linking The Statistical and Sociological Imaginations • Social reality is normative: interpretation depends on the place, time, and culture • Statistical norms are measurements of social norms • Statistical ideals often reflect social values © 2008 McGraw-Hill Higher Education

  7. Tools for Proportional Thinking • Data: Systematically acquired information, following the procedures of science and statistics • Statistical error: Known degrees of imprecision in procedures used to gather information © 2008 McGraw-Hill Higher Education

  8. Two Purposes of Statistics • Descriptive statistics: Used to tell us how many observations were recorded and how frequently each score or category occurred • Inferential statistics: Used to show cause and effect relationships and to test hypotheses and theories © 2008 McGraw-Hill Higher Education

  9. What is Science? • Science is the systematic study of empirical phenomena • Empirical means observable and measurable • Phenomena are facts, happenstances, events, or circumstances © 2008 McGraw-Hill Higher Education

  10. The Purpose of Science • The purpose of scientific investigation is to explain things • These explanations take the form of theory : A set of interrelated, logically organized statements that explain a phenomenon of special interest, and that have been corroborated through observation and analysis © 2008 McGraw-Hill Higher Education

  11. The Limitations of Science • Restricted to examining empirical phenomena • Many sound, factually based scientific arguments lack political or taxpayer support • Ethical dilemmas often arise creating resistance to its application © 2008 McGraw-Hill Higher Education

  12. Data and Variables • Data: Systematically acquired information • Variables: Measurable phenomena that vary or change over time, or that differ from place to place or from individual to individual • Constants: Characteristics of study subjects that do not vary © 2008 McGraw-Hill Higher Education

  13. Study subjects • Study subjects: The people or objects under scientific observation • Variation: How much the measurements of a variable differ among study subjects © 2008 McGraw-Hill Higher Education

  14. A Hypothesis • A prediction about the relationship between two variables, asserting that differences among the measurements of an independent variable will correspond to differences among the measurements of a dependent variable © 2008 McGraw-Hill Higher Education

  15. Independent and Dependent Variables • Dependent variable: The variable whose variation we wish to explain • Independent variables: The predictor variables that are related to, or predict variation in, the dependent variable © 2008 McGraw-Hill Higher Education

  16. Relationships Between Independent and Dependent Variables • Cause → Effect • Predictor → Outcome • Stimulus → Response • Intervention → Result (action taken) • Correlation: measures of the two variables fluctuate together © 2008 McGraw-Hill Higher Education

  17. The Research Process • Involves organizing ideas into a theory, making empirical predictions that support the theory, and then gathering data to test these predictions • Cumulative process – a continual process of accumulation of knowledge © 2008 McGraw-Hill Higher Education

  18. 7 Steps of the Research Process • Specify the research question • Review the scientific literature • Propose a theory and state hypotheses • Select a research design • Collect the data • Analyze the data and draw conclusions • Disseminate the results © 2008 McGraw-Hill Higher Education

  19. Mathematical Proportions • Division problems that weigh a part (the numerator) against a whole (the denominator) • Proportional thinking: placing an observation into a larger context • A sense of proportion: to see things objectively, make fair judgements about behavior, and give the correct amount of attention to things that really matter © 2008 McGraw-Hill Higher Education

  20. Calculating Proportions and Percentages • Start with a fraction • Divide the fraction to obtain a proportion (in decimal form) • The quotient will always have values between 0 and 1 • Multiply the proportion by 100 to change it into a percentage © 2008 McGraw-Hill Higher Education

  21. Transforming Fractions, Proportions, and Percentages • To change a fraction into a proportion: Divide to “decimalized” • A proportion into a percentage: Multiply by 100 • A percentage into a proportion: Divide the percentage by 100 • To express a proportion as a fraction: Observe the decimal places (See Appendix A) © 2008 McGraw-Hill Higher Education

  22. Rates • A rate is the frequency of occurrence of a phenomenon per a specified, useful “base” number of subjects in a population • Rate of occurrence = (p) (a base number) • Rates standardize comparisons for “populations at risk” • The choice of a base number depends on the phenomenon being measured © 2008 McGraw-Hill Higher Education

  23. Presenting Answers to Encourage Proportional Thinking Symbol = Formula = Contents of formula = Answer © 2008 McGraw-Hill Higher Education

  24. How to Succeed in This Course and Have Fun • Never miss class and keep up • Organize materials in a three-ring binder • Use proper reading techniques • Closely follow formulas, calculation spreadsheets, and procedures • Ask for assistance as it is needed © 2008 McGraw-Hill Higher Education

  25. Statistical Follies • Watch out for small denominators, especially when “percentage change” data is reported • A few new cases in a small group can appear as a large percentage change © 2008 McGraw-Hill Higher Education